Under the fixed-fitness Moran process [1]}, increasing the size \(N\)  of a finite population always leads to a decrease of the probability that a single mutant has of fixating in the whole population. When frequency-dependent fitness is introduced [2]}, despite this not being necessarily true, it is still observed to happen often. To probe the \(2\times 2\)  games under which \(\rho _{N+1}>\rho _N\)  is always true, we obtain Theorems 1 and 2.
